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OCR for page 41
41
APPENDIX B
ANALYSES OF SOUND SPECTROGRAMS OF "HOLD EVERYTHING..."
B-1. Time and Frequency Analysis
Several sound spectrograms were made of the first and second halves of
the "hold everything..." expression on Channels I and II. Two of these
pairs are given in Figures B-l and B-2. Although some similar features can
be observed in comparing the two channels in Figures B-1 and B-2, it is
difficult to tell if the similar features occur somewhat at random or if
corresponding features occur at corresponding times over the entire 3 1/2
second duration of the message, as must be the case if the corresponding
features are associated with the same transmission. For this reason, the
following analysis was made of two successive pairs of sound spectrograms
which were butted together, with an overlapping sound spectrogram being
used to ensure that the sound spectrograms were combined properly. The
result is shown in Figure B-3.
Twenty-seven corresponding features have been marked on Channels I and
II in Figure B-3. Since the timings of the corresponding features were to
be studied later, two observers were used in the identifications to
diminish the danger that human prejudice on the timing would affect the
identification. The first observer, looking at the sound spectrograms of
both Channels I and II but making no measurements, marked on Channel II 27
points which he felt were sufficiently characteristic and sufficiently well
reproduced on Channel I to be identifiable there by an independent
observer. Then a series of 27 xerographic copies were prepared of
different portions of Channel II, extending 1/2 second to each side of the
single identified characteristic and with no indication of time scale on
any of the Channel II strips. These strips and the Channel I sound
spectrogram were presented to a second observer who was asked to mark on
the Channel I sound spectrogram what he considered to be the most similar
characteristic to the one marked on each Channel II strip. He was asked to
do so by pattern recognition and not by measurement. His marks located the
black dots on the Channel I tape of Figure B-3. It was found that the
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42
second observer correctly identified 26 out of the 27 characteristics. In
the one case of disagreement (characteristic I) the second observer
subsequently agreed that the intended identification was better than the
one he selected.
Only after all the identifications had been made were the times and
frequencies of each characteristic measured and recorded in Table B-1.
These are plotted in Figure 4. It can be seen that the points fall
markedly close to a straight line with the only exception being the
misidentified characteristic I.
OCR for page 43
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I I I I I I I I I I t I I I I
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|| ~ ~ ~ ~ ~ ~ ~ e ~ e ~ ~ ~ ~ ~ ~ ~ e e e ~ ~ ~ e ~ ~ e
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1 1 1 1 1 1 1 1 1 1 1 ' ' 1 1
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O O O O O 0 00 ~ O O O O O O O O O O O O O O 0 00 0
11 r~ ~ e ~ ~ ~ ~ ~ ~ ~ e ~ ~ ~ ~ · ~ · ~ ~ e
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1 1 1 1 1 1' 1 1 1 1 1 1 1
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00 ~ ~ ~ ~ ~ ~ O ~ ~ L~ O ~ ~ c~ ~ ~ ~ 00 ~ ~ ~ ~ c~
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e e ~ ~ ~ e ~ ~ ~ e e e e e e e e e e e e e e e ~ e
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V ~ O ~ O ~ ~ CO 00 ~ ~ ~ C~ ~ ~ ~ ~ ~ ~ C~ ~ ~ ~ ~ C~
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OCR for page 44
44
A straight line of the form
T' = ~ + IT" ~ u
was fit to the (T', T") data. Under the copy hypothesis that the signal on
Channel I is a noisy copy of that on Channel II, the values of u are determined
by measurement errors in the presence of noise,and there may occasionally be an
outlier due to the matching noncorresponding features on the two channels.
The robust linear regression routine RLIN in the Minitab 80.1 interactive
statistical package yields the estimated fit
I' = - 0.0253 + 1.0599T" + u*
A sequence of regressions in which outliers are dropped one or two at a time
yields the fit
T' = - 0.0216 + 1.0593T" + u.
Here,the points 9, 11, 13, 18, and 19 were dropped. The standard deviation
of the fitted residuals of the remaining 22 points (adjusted for 20 degrees
of freedom) is s = 0.0092 and the estimated standard deviations of the two
coefficients above are 0.0037 and 0.0016, respectively.
The five outliers in the column labeled u = AT are marked with a D. All
other values of u are less than 0.015 in absolute value.
The ratios R = F"/F' of the measured frequencies at the paired points
in the two channels were computed. A sequence of averages in which outliers
are dropped eliminates four ratios numbered (1,5,8,13) and yields an average
R = 1.064 and standard deviation sR = 0.0272. R is an estimate of 6. The
standard deviation of R is oR/~i = 0.0058 so that R is a less accurate estimate
of ~ than that derived from the regressions above. The values of
v = R - 1.064 = AR
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45
are listed with the outliers marked by a D. Finally we calculate and list
1.0593 F
Except for the two outliers, marked D, corresponding to points (1,5) all of
the values of AF are less than 0.09 kHz in absolute value and have a sample
mean of -6.92 Hz and standard deviation of 48 Hz.
These data are consistent with the copy hypothesis, a probability of about
1/4 or less of an incorrect match and relatively small measurement errors in
the time and frequency measurements. To be more specific, let us suppose
(i) that the Channel II markings are precise, (ii) the Channel I markings may
be either wrong or correct, but displaced by an amount due to the noise, and
(iii) each measurement has a reading error.
For example suppose
t' = ~ + Ot" + u
T' = t' + u'
e
T" = t" ~ u"
e
n
where t' and t" are the exact times of the corresponding events, u is the
contribution of the distortion due to noise, T' and I" are the observed times,
and ue and u" are the reading errors. Then
~ ( n e ~ e) ~ FT + T
and, assuming independence of the residuals,
c, = o2 + (1 + ~2' ~2
n
~ ~ + 2~2
. u u
e n e
(The lack of statistical independence between T" and u = AT raises a technical
problem which is minor in the present context and won't be discussed here).
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46
Because the process of discarding outliers tends to bias the estimated
standard deviation downwards, one would expect ~ to be about 0.01 which is
consistent with ou ~ 0.005 and ou ~ 0.007, although other combinations are
also plausible considering,the data and the measurement techniques. The
five outliers, one of which is much larger than the others,suggest that the
probability of incorrect match may be as large as 1/4.
A similar analysis may be applied to the frequencies. If we write
—1
f' = ~ f" +v
F" = f" TV"
e
F' = f' +v'
e
n
where f' and f" are the exact frequencies, v is the contribution of the
distortion due to noise, F' and F" are the observed frequencies, and v'
and v'e are the reading errors. Then
F11
F = F. = ~ +AR
where the probability distribution of v = AR can be approximated by one
with mean O and standard deviation
(f')~l[62~2 + (~+62) 2 ]1/2 [a2 + 2 2 ]~/2/f,
n e n e
which averages out to approximately [(F') ][o + 2o ] / where [(F') ]
is the average of the (F') values. Also n e
AF = F' - 6~1F..
has mean O and standard deviation
2 + ~2 [1+~-2]~1/2 ~ [~2 + 2
e n e
and
~ ~ (F.~1~o
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47
the relation
CAR ~ (F' HALF
is approximately maintained by the estimates.
Could the observed coincidences have occurred even if the message
on Channel I were not a copy of that on Channel II? Suppose that as an
alternative hypothesis we assume that it alas a different message and the
time coincidences took place because the features marked maxima, minima,
flats,and downward slopes occur frequently on Channel I and a similar
feature could, at random, be close by to one being sought. For example,
there are 18 peaks in a 3.6 second interval. Thus at random, peaks would
occur at an average spacing of 0.2 seconds and, according to the Poisson
process calculation, the probability of at least one peak within a time
of ~ seconds from a specified time would be p = 1 -e / .
The frequencies of the other features are no greater than that
of peaks; hence, the probability of a coincidence within |AT| < 0.015 is
p =1 -e =0.14. We have 22 such coincidences out of 27 trials.
Granted that we selected estimates of ~ and ~ to increase the number of
such coincidences, we may, to be conservative, eliminate two of these
coincidences. We then have 20 out of 25 coincidences. Assuming inde-
pendence, the number of such coincidences has a binomial distribution
with mean 25 x(0.14) =3.5 and standard deviation 1.73. Then 20 is 9.S1
standard deviations away from the mean and the probability of getting as
many as 18 coincidences is about 2.1 xlO .
Note that 25 of 27 values of AF are less than 0.1 kHz in absolute
value. If each of these AF were uniformly distributed over a narrow
range of +0.3 kHz, the probability of 25 or more independent absolute
values less than 0.1 would be very small (2 xlO ). In fact, this
probability would be 0.001 even if the range of values of AF were cut in
half to +0.15 kHz.
The sound spectrograms shown in Figure 4 are similar to those in
Figure B-3 except that one recording is slowed down 6.7% to bring the
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48
ratio of apparent recorder speeds closer to unity. The black dots indicate
the same features as in Figure B-3 except for a few points, such as I, that
have been adjusted for a better fit in Figure 4.
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49
B-2. Meausrements of Easily Identified Frequency Ratios on sound
Spectrograms
A casual inspection of the original sound spectrograms of sections of
Channel I and Channel II recordings for the time interval identified as
containing the phrase "hold everything..." show marked similarities, but
with the most clearly defined frequencies on Channel I being somewhat lower
than those on corresponding sections of Channel II. Since the analysis of
the preceding section shows that the measured times between corresponding
events on Channel I are longer than on Channel II, by about 6%, it seemed
worth measuring the frequency ratios of corresponding signals that were
particularly well suited for frequency measurement; if the two sound
spectrograms really did originate from a single 3.5 second long signal on
Channel II, which was fed by cross talk onto Channel I, then the frequency
ratio must depart from unity by that same approximately 6%. This was our
working hypothesis at the time, so the frequency ratio measurements
provided a test of the hypothesis - if the frequency ratio was not
approximately 1.06 the hypothesis would have been totally disproved.
One of the Committee members, therefore, measured the frequency ratio
at five corresponding sections of the records. The sections to be measured
were selected by a simple criterion that can be used by any interested
person. The frequency must stay constant (a horizontal band, by visual
inspection) for at least 1/30 second, and it must be clearly visible on
both channels at corresponding times. It is not required that the
frequency bands originate from speech components of the signals on Channel
II. Anyone listening to this section of Channel II will hear, in addition
to the sentence starting with "Hold everything secure...," a number of
tones that are both amplitude and frequency modulated. These tones are as
useful as the speech components in proving that a signal on Channel II was
imprinted by cross talk onto Channel I at the time of the conjectured
"shots".
The above mentioned criterion was satisfied by five sections of the
two tapes, which are identified by their original times I', on Channel I.
They are as follows:
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50
Section
Time
1 centered at T' = 0.67 seconds
2 " = 2.19 "
3.13 11
3.31 1'
3.52 11
3
4
-
The measurement of each frequency was made in the following way: an
indentation was made in the surface of the glossy print, near the center of
each "band," with a sharp point. The observer then looked at the mark, to
check that it was as nearly centered as possible in the vertical direction.
On the few occasions that it appeared to be above or below the center of
the band, a new mark was made, and checked to be adequately centered. Only
after the observer was satisfied that he had placed ten marks correctly --
one for each of five bands, on two spectrograms -- did the measurements
begin. The measurement consisted of a linear interpolation between
adjacent kilohertz lines using a millimeter scale as the measuring device.
The following five ratios came out of the measurements just as described:
Section Frequency Ratio
2
3
4
5
1.054
1.066
1.065
1.052
1.067
Mean Value 1.061+0.007
This value is consistent with the time ratio 1.059+0.002 found
from the slope of the line relating the time coordinates on the two
channels in Figure 5.
Another Committee member made independent measurements of the average
of the same frequency ratios and found a mean value of 1.063 + 0.007
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In view of the close agreement between this pair of independent
measurements, we conclude that the mean frequency ratio is
R = 1.062+0.007
.
The excellent agreement between the time-derived, and the
frequency-derived ratio of tapes speeds lends strong support to the
hypothesis that the "hold eveything..." signals observed on Channel I were
imprinted by cross talk from Channel II.
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B-3. ALTERNATIVE TIME AND FREQUENCY ANALYSES OF SOUND SPECTROGRAMS
The analyses in Appendixes B-1 and B-2 may be subject to some criticism.
A certain amount of subjectivity derives from the fact that the first observer
was looking at the sound spectrograms from both channels while he marked
points on Channel I. The strips in Channel II were one second wide, which is
a substantial portion of the entire 3.5 second spectrogram. Consequently
the 27 strips had large overlapping parts. To the extent that observer 2
recalled what he did on previous matches or to the extent that he used the
same cues in the overlapping portions, the resulting times were dependent
observations. A theory that uses estimates and conclusions based on independ-
ence assumptions may overestimate the significance or accuracy of these
conclusions and estimates.
However, this experiment was supplemented by several variations that
derived similar results. Some of these were more careful to avoid the subjec-
tivity and to reduce considerably the dependence aspects of the experiment
presented here. These are not reported in detail, because they were car-
ried out using xerographic copies of photographs using several scales, and
relatively crude measuring instruments (graph paper in place of rulers). A
presentation here would be more complex and the photographs would lack clarity.
a) Initial experiments
In chronological order, an initial experiment was carried out where 28
pairs of corresponding points were measured on both Channel I and Channel II
by an observer who studied both spectrograms simultaneously for characteristic
features. A least squares analysis of these highly subjective data gave the
fitted relation
T' = - 0.0409 + 1.0673T"
and the ratios of the observed frequencies
R = F"/F'
averaged to 1.0728.
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A "robust" analysis of the pairs (T', T") in the first experiment, where
three outliers were discarded, gave the estimated relation
T' = - 0.0235 + 1.0633 T" + u
where the residual u had estimated standard deviation 0.0159 and the estimated
standard deviation of the coefficient ~ of T" was 0.0028.
An alternate robust linear regression, implemented on the Minitab-1980
interactive statistical packages under the command RLIN, gave
T' = - 0.0295 ~ 1.0626T'1 + u
A second experiment was by an observer who measured the central frequen-
cies of 5 distinct pairs of broad horizontal sections appearing at com-
parable times and with relatively high frequencies. The ratios of these
central frequencies R averaged R = 1.060 and had sample standard deviation
0.0072.
b) A more objective experiment on the timing
At this point a more objective procedure was carried out using xero-
graphic copies of a reduced photograph of the spectrograms. The observer was
given the experimenter's explanation of the theory that messages were broad-
cast on Channel II and picked up by the stuck microphone located near a
receiver of Channel II. The observer was shown copies of Channel I and II for
two other messages that had been well duplicated; Y - "You want...Stemmons"
and S - "Says they came from...." It was explained that dark portions meant
loud signals and sharp changes that were dark would probably be well repro-
duced under the theory. The observer was asked to mark about 20 spots on
Channel II that would be likely to be well reproduced. The observer was not
given an opportunity to study Channel ~ of H - the spectrogram suspected of
being "Hold everything secure...."
Twenty strips of Channel II of a, each between 0.2 and 0.3 seconds long,
were reproduced by Xerox with the marked point in the center. The estimate
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T = -0. 0402 + 1. 0673T" was used to locate corresponding points on Channel I.
Strips of a Xerox of Channel I were cut out. These strips were 3/4 second
long and were centered at a point displaced from T by a random quantity
uniformly distributed on the interval (-.3, .3) in seconds. Corresponding
strips were -paired and these pairs were arranged in random order.
A second observer was asked to align the two strips of each pair and to
locate on Channel I a vertical mark corresponding to the time of the mark in
Channel II. This observer was allowed to use as much context as was available,
in the approimxately 0.3 second of Channel II and 0.75 seconds of Channel I
in the pair, to help him make the mark. It was not necessary for him to find
a feature corresponding to the point marked. He, too, had the theory explained
to him, and he was informed that there might be a consistent difference in
the frequencies on the two channels.
This experiment requires some balance in selecting the widths of the
strips. If both strips are too narrow, one is bound to get (T', T") points
that lie close to the line I' = 1.0673T" - 0.0404 and a good fit will not
be convincing. If the strip on Channel ~T is too narrow and that of Channel I
is very wide, it will be very easy for the observer to be misled by similar
characteristics elsewhere. This would reduce the efficiency and power of
the experiment. If the strip on Channel II is widen then the different
strips will overlap substantially and memory and the cues the observer uses may
make results on different strips dependent. As the experiment was carried out
the 20 strips of Channel II had pairs with some overlap, but in the random order
of presentation these small strips looked quite distinct.
When the times were measured, the deviations, AT = I' - (1.0633T" - 0.0235),
between the measured time in Channel I and the time anticipated by the robust
estimate of the straight line, were calculated. Thirteen of these were no larger
than 0.054 seconds, one was 0.075 seconds and the remaining 6 of 0.203 seconds
or more. The mean and standard deviation of the thirteen smaller deviations
were -0.016 seconds and 0.026 seconds. The root mean square deviation was 0.029
seconds.
These results are consistent with the copy hypothesis if one anticipates
misclassifications about 1/4 of the time and measurement error due to noise
and measurement accuracy of about 0.03 second (about 0.07 inch on the scales
used).
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Under the randomness alternative hypothesis, that the two messages are
unrelated and any matching of features is randomly located, one may estimate
that the probability of being within 0.054 seconds of the expected point to be
about 0.2.* The number of such coincidences out of 20 independent trials
would be binomially distributed with mean 4 and standard deviation 1.79 and
13 successes corresponds to (13-4-.5)/(1.79) = 4.75 standard deviations from
the mean and is highly unlikely.
Moreover, subtracting 2 of the 13 successes to compensate for the choice
of the linear fit would still make this match very unlikely. Then we would have
(11-4-.5)/1.79 = 3.63 standard deviations with P = 0.0006.
The poor quality of the xerographic copies with which this experiment was
carried out and the low-quality measuring instruments explain in part why
the standard deviation of the observed discrepancies were much larger than
those observed with the data presented in Table B-1.
c) A more objective experiment on the frequencies
The experimenter selected 14 dark horizontal bands on a Xerox copy of
Channel II. The time points T" of these horizontal bands were measured. Correspond-
ing times on ChannelI given by T = 1.0633T" - 0.0225 were located. The subject
was requested to mark the central frequency of the bands on Channel II. Then
the subject was requested to locate bands on Channel ~ at the times marked and
to mark the central frequency.
These central frequencies were measured and labeled F1 and F2 for the two
channels. The ratio R = F2/F1 was calculated and ranged from 1.337 to 1.024.
Deleting 4 outliers, the average was R = 1.0665 and the sample standard deviation
was Sp = 0. 0116.
under one randomness hypotheses, the distribution of the discrepancy corresponds
to the sum of the off center random displacement (uniform from -.3 to .3) and
an independent random choice in (-.375, .375) along the Channel I strip. Since
this latter choice is almost uniform except for a possible bias toward the center,
it was modeled as the sum of two uniforms from (-.3 to .3) which has a symmetric
triangular distribution from -.6 to .6. The probability that this sum is between
-.054 and +.054 is
1 ( 6- 054) = 0.17 < 0.2.
.6 _
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These data are consistent with a hypotheses that Channel I is a noisy version
of Channel II which leads to a wrong pairing about 1/3 of the time and that when
the correct pairing is made, the noise distortion and measurement error in the
individual central frequency readings corresponds to about F2sR/~7 = 0.015 kHz
or about 15 Hz.
By no stretch of theimagination could these readings be consistent with
a purely random location of horizontal bands theory. Even a much more restric-
tive hypothesis, assuming that another speech was uttered in a similar cadence
with similar frequencies of vowels end mechanisms yielding strong horizontal bands,
was shown to be implausible as long as these bands were allowed to fluctuate
at random within narrow ranges determined by the empirical data.
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B-4. Digital Calculations of Cross Correlations Between Channel I and
Channel II
If indeed "hold everything..." on Channel II was transmitted to and
recorded on Channel I at the time occupied by the assumed "shots", then the
digital cross-correlation of the short-time acoustic (energy) spectra of
the two Channels should show a correlation substantially larger than that
which would be achieved by chance. This was studied by a member of the Com-
mittee end two collaborators. The Channel I and Channel II recordings were
digitized and the short-term acoustic spectra were taken and stored in a
digital computer. The printouts of these spectra are shown in Figures B-4,
B-5 and B-6. These digital spectrograms were computed directly from
magnetic tapes and did not involve the use of the FBI sound spectrogram
equipment.
An objective measure of similarity of two spectral matches is obtained
from the cross correlation coefficient, defined as for the functions X and
Y by
ccc = (T X.Y)/~Z X~X)~E y y)21/2
This cross correlation coefficient would be reduced if one of the
recordings were played at the wrong speed, or if the recording at one time
were compared with the same or a different recording at a different time.
The first cross correlation coefficients were made from the same
Channel I and II recorded copies that were used in preparing Figures 3, 4,
B-1, and B-2. It was found that the biggest peak for the cross correlation
coefficient occurred for a relative warp (or speed ratio) of 1.06 in
agreement with the other two manual approaches for comparing Channels I and
II, a1% deviation of warp from optimum diminished the peak substantially.
Unfortunately, that Channel II copy contains many repeats caused by the
Gray Audograph machine in playback. Accordingly another tape copy was
prepared by members of the Committee directly from the original Audograph
plastic disk itself and by the use of a standard turntable and tone arm,
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thus producing a tape without compensation for the fact that the disk was
originally recorded at constant linear track speed. It was this tape that
was used in preparing the sound spectrograms shown in Figures B-4, B-5, and
B-6. The Channel II signals are from the 7.5 ips tape recording of the
Gray Audograph record played on a turntable (12/9/81~. The tape was played
at 3.75 ips when digitized for these experments: hence, the rate of change
of the correction factor was assumed to be half the measured rate of 0.0005
per second. The signals were digitized at 20000 samples per second, and a
400-pt Fourier transform was computed every 200 samples (10 millisec),
using a 400-pt Blackman window. The correlations were performed on
portions of the 200-pt spectra, which have a point spacing of 50 Hz. The
high frequencies of the Channel I spectra were boosted at a rate of 6 db
per lOOO Hz and then normalized to a constant energy in the band of
interest.
Figure 6 gives the cross correlation coefficient for the "hold
everything..." segments when the relative speed was selected to give the
largest peak that occurred when the Channel II signal was sped up slightly
by compressing the time scale by a factor that varied from 0.957 to 0.961
(changing at the rate of 0.00025 per see). Figure 6 is a plot of the 750
correlation coefficients obtained by sliding 2.50 sees of Channel I along
10.00 sees of Channel II, 0.01 sees at a time, using frequencies in the
band 600 Hz to 3500 Hz. For comparison the cross correlation coefficients
of the unambiguous segment "You want...Stemmons" are plotted in Figure 7
with the time scale of Channel II stretched by a factor that varied from
1.013 to 1.015. The shape of the peak is vey similar to that for the "hold
eveything..." segment. The background is somewhat smoother simply because
there is less noise in Channel I at this time. Channel I, however, in
neither case gives a perfect reproduction of Channel II. It has lost some
of the high and low frequencies and, as one would expect, there are tones
present on Channel I that are not on Channel II.
The marked narrow peaks of the cross correlation curves clearly show
by an objective test that the "hold everything..." segment of Channel II is
present on Channel I at the same location as the acoustic impulses.
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Inspection of the spectrograms of Figure B-6 shows the presence of a
ChannelII brief tone beginning at time 32.00 sees and extending to 32.08
sees. It resumes at time 32.24 and disappears once more at 32.43. The
ChannelII brief tone is clearly visible in the Channel I spectrogram
aligned by the relative timing obtained from Figure 6. A strong Channel I
heterodyne is observed to begin at time 32.03 and to end at 32.17 sees.
The resumption of the ChannelIT brief tone in Channel I at 32.24 sees is
clearly weak and gradually grows in strength. These observations can be
made more quantitatively from Figures B-7 and B-8, which are "printer
plots" of the relevant regions of the Channel II and Channel I spectra.
The vertical bars outlining the Channel lI brief tone (and the same
time-frequency bins in Channel I) not only guide the eye, but allow the
quantitative calculation of the energy between the bars. The digits
printed are the "bin energy" in decibels, each unit corresponding to a 4-db
range. By the end of the first Channel II brief tone at time 32.0B, it has
been suppressed by about 10 db relative to its value before the Channel I
heterodyne appeared at 32.03. When the Channel IT brief tone reappears at
30.24 sees, the AGC has suppressed it by approximately 20 db, and it
recovers to its original value only at about 32.43 sees, some 0.26 sees
after the end of the Channel I heterodyne at 32.17 sees. That this AGO
action is not due to a later recorder or a re-recording is demonstrated by
the fact that much stronger ChannelII brief tones are present on the
Channel I recording, without showing the drop in intensity which is induced
by the Channel Iheterodyne.
Representative terms from entire chapter:
cross correlation
